How to choose between two uncertainty calculation method?

Hello,
I have made an experimental work and I am ask to provide a formal experimental error analysis. I have a difficulty to choose the appropriate analysis way and would like to have some advices or explanations.
I have measured a temperatures at the intlet (Ti) and outlet (To) of a heat exchanger and the mass flow rate of the fluid. I can calculate the power:
Q = mC (To-Ti)
From what I learn on uncertainty calculations, I am a little bit confused. I finally found that I could calculate my uncertainty in two ways:
(1): [itex]\frac{ΔQ}{Q}[/itex] = [itex]\frac{Δm}{m}[/itex]+ [itex]\frac{2ΔT}{To-Ti}[/itex]

(2): [itex]\frac{ΔQ}{Q}[/itex] =[itex]\sqrt{\left(\frac{Δm}{m}\right)^2+\left(\frac{2ΔT}{To-Ti}\right)^2}[/itex]

Δm: accuracy of the mass flowrate meter (documentation of the supplier)
ΔT: accuracy of the mass flowrate meter (value given by the calibration center)
C is admit as a constant

I made just one measurement. Which one of the above equations must I use and why?

Actually, I derived heat transfer coefficients (built a curve) from several measurements, by changing the flowrate m and the inlet temperature Ti. But no test has been repeated in the same conditions. Is the first method or the second one am I going to use for the "error analysis"?
Thank you in advance.
P.S. Please, even if you do not have a time, even a short answer would be useful for me.

 

Thank you ImaLooser for your explanation. I assume that the accuracies are independant. But I don't know if the accuracy of the intruments are standard deviation (I always think that they are the maximal error; I may be wrong). Actually, for a long time, I do not realise that the accuracy of an instrument can be given as a standard deviation. So, in case, it is the maximal error, should I keep equation (2)?
Thank you.

 

Thank you very much. I understand now the difference.